Pseudopotential plane-wave density functional theory (NWPW)

The NWChem plane-wave (NWPW) module uses pseudopotentials and plane-wave basis sets to perform Density Functional Theory
calculations (simple introduction Media:Pw-lecture.pdf). This module complements the capabilities of the more traditional Gaussian function based approaches by having an accuracy at least as good for many applications, yet is still fast enough to treat systems containing hundreds of atoms. Another significant advantage is its ability to simulate dynamics on a ground state potential surface directly at run-time using the Car-Parrinello algorithm. This method's efficiency and accuracy make it a desirable first principles method of simulation in the study of complex molecular, liquid, and solid state systems. Applications for this first principles method include the calculation
of free energies, search for global minima, explicit simulation of solvated molecules, and simulations of complex vibrational modes that cannot be described within the harmonic approximation.

Band - A band structure code for calculating crystals and surfaces with small band gaps (e.g. semi-conductors and metals).

PAW - a (gamma point) projector augmented plane-wave code for calculating molecules, crystals, and surfaces (This module will be deprecated in the future releases since PAW potentials have been added to PSPW)

The PSPW, Band, and PAW modules can be used to compute the energy and optimize the geometry. Both the PSPW and Band modules can also be used to find saddle points, and compute numerical second derivatives. In addition the PSPW module can also be used to perform Car-Parrinello molecular dynamics.
Section PSPW Tasks describes the tasks contained within the PSPW module, section Band Tasks describes the tasks
contained within the Band module, section PAW Tasks describes the tasks contained within the PAW module, and section Pseudopotential and PAW basis Libraries describes the pseudopotential library included with NWChem. The datafiles used by the PSPW module are described in section NWPW RTDB Entries and DataFiles. Car-Parrinello output data files are described in section Car-Parrinello Output Datafiles, and the minimization and Car-Parrinello algorithms are described in section Car-Parrinello Scheme for Ab Initio Molecular Dynamics. Examples of how to setup and run a PSPW geometry optimization, a Car-Parrinello simulation, a band structure minimization, and a PAW geometry optimization are presented at the end. Finally in section NWPW Capabilities and Limitations the capabilities and limitations of the NWPW module are discussed.

As of NWChem 6.6 to use PAW potentials the user is recommended to use the implementation contained in the PSPW module (see Sections ). PAW potentials are also being integrated into the BAND module. Unfortunately, the porting to BAND was not completed for the NWChem 6.6 release.

If you are a first time user of this module it is recommended that you skip the next five sections and proceed directly to the tutorials.

PSPW Tasks - Gamma Point Calculations

All input to the PSPW Tasks is contained within the compound PSPW block,

PSPW
...
END

To perform an actual calculation a TASK PSPW directive is used (Section Task).

Once a user has specified a geometry, the PSPW module can be invoked with no input directives (defaults invoked throughout). However, the user will probably always specify the simulation cell used in the computation, since the default simulation cell is not well suited for most systems. There are sub-directives which allow for customized application; those currently provided as options for the PSPW module are:

MULT - optional keyword which if specified allows the user to define the spin multiplicity of the system

MULLIKEN - optional keyword which if specified causes a Mulliken analysis to be performed at the end of the simulation.

EFIELD - optional keyword which if specified causes an atomic electric field analysis to be performed at the end of the simulation.

ALLOW_TRANSLATION - By default the the center of mass forces are projected out of the computed forces. This optional keyword if specified allows the center of mass forces to not be zero.

TRANSLATION - By default the the center of mass forces are projected out of the computed forces. TRANSLATION ON allows the center of mass forces to not be zero.

ROTATION - By default the overall rotation is not projected out of the computed forces. ROTATION OFF projects out the overal rotation of the molecule.

CG - optional keyword which sets the minimizer to 1

LMBFGS - optional keyword which sets the minimizer to 2

SCF - optional keyword which sets the minimizer to be a band by band minimizer. Several options are available for setting the density or potential mixing, and the type of Kohn-Sham minimizer.

<mapping> - for a value of 1 slab FFT is used, for a value of 2 a 2d-hilbert FFT is used.

A variety of prototype minimizers can be used to minimize the energy. To use these new optimizers the following SET directive needs to be specified:

set nwpw:mimimizer 1 # Default - Grassman conjugate gradient minimizer is used to minimize the energy.
set nwpw:mimimizer 2 # Grassman LMBFGS minimimzer is used to minimize the energy.
set nwpw:minimizer 4 # Stiefel conjugate gradient minimizer is used to minimize the energy.
set nwpw:minimizer 5 # Band-by-band (potential) minimizer is used to minimize the energy.
set nwpw:minimizer 6 # Projected Grassman LMBFGS minimizer is used to minimize the energy.
set nwpw:minimizer 7 # Stiefel LMBFGS minimizer is used to minimize the energy.
set nwpw:minimizer 8 # Band-by-band (density) minimizer is used to minimize the energy.

Limited testing suggests that the Grassman LMBFGS minimizer is about twice as fast as the conjugate gradient minimizer. However, there are several known cases where this optimizer fails, so it is currently not a default option, and should be used with caution.

In addition the following SET directives can be specified:

set nwpw:lcao_skip .false. # Initial wavefunctions generated using an LCAO guess.
set nwpw:lcao_skip .true. # Default - Initial wavefunctions generated using a random plane-wave guess.
set nwpw:lcao_print .false. # Default - Output not produced during the generation of the LCAO guess.
set nwpw:lcao_print .true. # Output produced during the generation of the LCAO guess.
set nwpw:lcao_iterations 2 #specifies the number of LCAO iterations.

PAW Potentials

The PSPW code can now handle PAW potentials. To use them the pseudopotentials input block is used to redirect the code to use the paw potentials located in the default paw potential library ($NWCHEM_TOP/src/nwpw/libraryp/paw_default). For example, to redirect the code to use PAW potentials for carbon and hydrogen, the following input would be used.

Most of the capabilities of PSPW will work with PAW potentials including geometry optimization, Car-Parrinello ab initio molecular dynamics, Born-Oppenheimer ab initio molecular dynamics, Metropolis Monte-Carlo, and AIMD/MM. Unfortunately, some of the functionality is missing at this point in time such as Mulliken analysis, and analytic stresses. However these small number of missing capabilities should become available over the next couple of months in the development tree of NWChem.

Even though analytic stresses are not currently available with PAW potentials unit cell optimization can still be carried out using numerical stresses. The following SET directives can be used to tell the code to calculate stresses numerically.

set includestress .true. #this option tells driver to optimize the unit cell
set includelattice .true. #this option tells driver to optimize cell using a,b,c,alpha,beta,gamma
set nwpw:frozen_lattice:thresh 999.0 #large number guarentees the lattice gridding does not adjust during optimization
set nwpw:cif_filename pspw_corundum
set nwpw:stress_numerical .true.
set nwpw:lstress_numerical .true.

PAW Implementation Notes

The main idea in the PAW method(Blochl 1994) is to project out the high-frequency components of the wavefunction in the atomic sphere region. Effectively this splits the original wavefunction into two parts:

The first part is smooth and can be represented using a plane wave basis set of practical size. The second term is localized with the atomic spheres and is represented on radial grids centered on the atoms as

where the coefficients are given by

This decomposition can be expressed using an invertible linear transformation, T, is defined which relates the stiff one-electron wavefunctions ψn to a set of smooth one-electron wavefunctions

which can be represented by fairly small plane-wave basis. The transformation T is defined using a local PAW basis, which consists of atomic orbitals, , smooth atomic orbitals, which coincide with the atomic orbitals outside a defined atomic sphere, and projector functions, . Where I is the atomic index and α is the orbital index. The projector functions are constructed such that they are localized within the defined atomic sphere and in addition are orthonormal to the atomic orbitals. Blöchl defined the invertible linear transformations by

The main effect of the PAW transformation is that the fast variations of the valence wave function in the atomic sphere region are projected out using local basis set, thereby producing a smoothly varying wavefunction that may be expanded in a plane wave basis set of a manageable size.

The expression for the total energy in PAW method can be separated into the following 15 terms.

The first five terms are essentially the same as for a standard pseudopotential plane-wave program, minus the non-local pseudopotential, where

The local potential in the term is the Fourier transform of

It turns out that for many atoms σI needs to be fairly small. This results in being stiff. However, since in the integral above this function is multiplied by a smooth density the expansion of Vlocal( / mathbfG) only needs to be the same as the smooth density. The auxiliary pseudoptential is defined to be localized within the atomic sphere and is introduced to remove ghost states due to local basis set incompleteness.

The next four terms are atomic based and they essentially take into account the difference between the true valence wavefunctions and the pseudowavefunctions.

The next three terms are the terms containing the compensation charge densities.

In the first two formulas the first terms are computed using plane-waves and the second terms are computed using Gaussian two center integrals. The smooth local potential in the Ecmp − vloc term is the Fourier transform of

The stiff and smooth compensation charge densities in the above formula are

where

The decay parameter σI is defined the same as above, and is defined to be smooth enough in order that ρ ̃_cmp (r) and can readily be expanded in terms of plane-waves.

The final three terms are the energies that contain the core densities

If these functionals are used in a publication please include in your citations the references to Grimme's work.

Using Exchange-Correlation Potentials Available in the DFT Module

(Warning - To use this capability in NWChem 6.6 the user must explicitly include the nwxc module in the NWCHEM_MODULES list when compiling. Unfortunately, there was too much uncertainty in how the nwxc computed higher-order derivatives used by some of the functionality in nwdft module to include it in a release for all the functionality in NWChem. We are planning to have a debug release in winter 2016 to take fix this problem. This capability is still included by default in NWChem 6.5)

These functional can be invoked by prepending the "new" directive before the exchange correlation potetntials in the input directive, XC new slater vwn_5.

That is, this statement in the input file

nwpw
XC new slater vwn_5
end
task pspw energy

Using this input the user has ability to include only the local or nonlocal contributions of a given functional. The user can also specify a multiplicative prefactor (the variable <prefactor> in the input) for the local/nonlocal component or total (for more details see Section XC and DECOMP -- Exchange-Correlation Potentials). An example of this might be,

XC new becke88 nonlocal 0.72

The user should be aware that the Becke88 local component is simply the Slater exchange and should be input as such.

Any combination of the supported exchange functional options can be used. For example the popular Gaussian B3 exchange could be specified as:

XC new slater 0.8 becke88 nonlocal 0.72 HFexch 0.2

Any combination of the supported correlation functional options can be used. For example B3LYP could be specified as:

Exact Exchange

Self-Interaction Corrections

The SET directive is used to specify the molecular orbitals contribute to the self-interaction-correction (SIC) term.

set pspw:SIC_orbitals <integer list_of_molecular_orbital_numbers>

This defines only the molecular orbitals in the list as SIC active. All other molecular orbitals will not contribute to the SIC term.
For example the following directive specifies that the molecular orbitals numbered 1,5,6,7,8, and 15 are SIC active.

The nwpw:dos:actlist variable is used to specify the atoms used to determine weights for dos generation. If the variable is not set then all the atoms are used, e.g.

set nwpw:dos:actlist 1 2 3 4

For projected density of states the "Mulliken" keyword needs to be set, e.g.

nwpw
Mulliken
dos
end

Point Charge Analysis

The MULLIKEN option can be used to generate derived atomic point charges from a plane-wave density. This analysis is based on a strategy suggested in the work of P.E. Blochl, J. Chem. Phys. vol. 103, page 7422 (1995). In this strategy the low-frequency components a plane-wave density are fit to a linear combination of atom centered Gaussian functions.

The following SET directives are used to define the fitting.

set pspw_APC:Gc <real Gc_cutoff> # specifies the maximum frequency component of the density to be used in the fitting in units of au.
set pspw_APC:nga <integer number_gauss> # specifies the the number of Gaussian functions per atom.
set pspw_APC:gamma <real gamma_list> # specifies the decay lengths of each atom centered Gaussian.

PSPW_DPLOT - Generate Gaussian Cube Files

The pspw dplot task is used to generate plots of various types of electron densities (or orbitals) of a molecule. The electron density is calculated on the specified set of grid points from a PSPW calculation. The output file generated is in the Gaussian Cube format. Input to the DPLOT task is contained within the DPLOT sub-block.

This sub-directive specifies the name of the molecular orbital file. If the second file is optionally given the density is computed as the difference between the corresponding electron densities. The vector files have to match.

By default the grid spacing and the limits of the cell to be plotted are defined by the input wavefunctions. Alternatively the user can use the LIMITXYZ sub-directive to specify other limits. The grid is generated using No_Of_Spacings + 1 points along each direction. The known names for Units are angstroms, au and bohr.

Band Tasks - Multiple k-point Calculations

All input to the Band Tasks is contained within the compound NWPW block,

NWPW
...
END

To perform an actual calculation a Task Band directive is used (Section Task).

Task Band

Once a user has specified a geometry, the Band module can be invoked with no input directives (defaults invoked throughout). There are sub-directives which allow for customized application; those currently provided as options for the Band module are:

The user enters the special points and weights of the Brillouin zone. The following list describes the input in detail.

<name> - user-supplied name for the simulation block.

<k1 k2 k3> - user-supplied values for a special point in the Brillouin zone.

<weight<> - user-supplied weight. Default is to set the weight so that the sum of all the weights for the entered special points adds up to unity.

Band Structure Paths

SC: gamma, m, r, x

FCC: gamma, k, l, u, w, x

BCC: gamma, h, n, p

Rhombohedral: not currently implemented

Hexagonal: gamma, a, h, k, l, m

Simple Tetragonal: gamma, a, m, r, x, z

Simple Orthorhomic: gamma, r, s, t, u, x, y, z

Body-Centered Tetragonal: gamma, m, n, p, x

Special Points of Different Space Groups (Conventional Cells)

(1) P1

(2) P-1

(3)

Screened Exchange

Density of States and Projected Density of States

Two-Component Wavefunctions (Spin-Orbit ZORA)

BAND_DPLOT - Generate Gaussian Cube Files

The BAND BAND_DPLOT task is used to generate plots of various types of electron densities (or orbitals) of a crystal. The electron density is calculated on the specified set of grid points from a Band calculation. The output file generated is in the Gaussian Cube format. Input to the BAND_DPLOT task is contained within the BAND_DPLOT sub-block.

This sub-directive specifies the name of the molecular orbital file. If the second file is optionally given the density is computed as the difference between the corresponding electron densities. The vector files have to match.

By default the grid spacing and the limits of the cell to be plotted are defined by the input wavefunctions. Alternatively the user can use the LIMITXYZ sub-directive to specify other limits. The grid is generated using No_Of_Spacings + 1 points along each direction. The known names for Units are angstroms, au and bohr.

Car-Parrinello

The Car-Parrinello task is used to perform ab initio molecular dynamics using the scheme developed by Car and Parrinello. In this unified ab initio molecular dynamics scheme the motion of the ion cores is coupled to a fictitious motion for the Kohn-Sham orbitals of density functional theory. Constant energy or constant temperature simulations can be performed. A detailed description of this method is described in section Car-Parrinello Scheme for Ab Initio Molecular Dynamics.

Input to the Car-Parrinello simulation is contained within the Car-Parrinello sub-block.

NWPW
...
Car-Parrinello
...
END
...
END

To run a Car-Parrinello calculation the following directives are used:

Nose-Hoover or Temperature - optional subblock which if specified causes the simulation to perform Nose-Hoover dynamics. If this subblock is not specified the simulation performs constant energy dynamics. See section -sec:pspw_nose- for a description of the parameters. Note that the Temperature subblock is just a reordering of the Nose-Hoover subblock.

SA_decay - optional subblock which if specified causes the simulation to run a simulated annealing simulation. For simulated annealing to work the Nose-Hoover subblock needs to be specified. The initial temperature are taken from the Nose-Hoover subblock. See section -sec:pspw_nose- for a description of the parameters.

<sa_scale_c> - decay rate in atomic units for electronic temperature.

<sa_scale_r> - decay rate in atomic units for the ionic temperature.

<xyz_filename> - name of the XYZ motion file generated

<emotion_filename> - name of the emotion motion file. See section EMOTION motion file for a description of the datafile.

<hmotion_filenameh> - name of the hmotion motion file. See section HMOTION motion file for a description of the datafile.

<eigmotion_filename> - name of the eigmotion motion file. See section EIGMOTION motion file for a description of the datafile.

<ion_motion_filename> - name of the ion_motion motion file. See section ION_MOTION motion file- for a description of the datafile.

MULLIKEN - optional keyword which if specified causes an omotion motion file to be created.

<omotion_filename> - name of the omotion motion file. See section [[#OMOTION motion file|OMOTION motion file] for a description of the datafile.

When a DPLOT sub-block is specified the following SET directive can be used to output dplot data during a PSPW Car-Parrinello simulation:

set pspw_dplot:iteration_list <integer list_of_iteration_numbers>

The Gaussian cube files specified in the DPLOT sub-block are appended with the specified iteration number.

For example, the following directive specifies that at the 3,10,11,12,13,14,15, and 50 iterations Gaussian cube files are to be produced.

set pspw_dplot:iteration_list 3,10:15,50

Adding Geometry Constraints to a Car-Parrinello Simulation

The Car-Parrinello module allows users to freeze the cartesian coordinates in a simulation (Note - the Car-Parrinello code recognizes Cartesian constraints, but it does not recognize internal coordinate constraints). The +SET+ directive (Section Applying constraints in geometry optimizations) is used to freeze atoms, by specifying a directive of the form:

set geometry:actlist <integer list_of_center_numbers>

This defines only the centers in the list as active. All other centers will have zero force assigned to them, and will remain frozen
at their starting coordinates during a Car-Parrinello simulation.

For example, the following directive specifies that atoms numbered 1, 5, 6, 7, 8, and 15 are active and all other atoms are frozen:

set geometry:actlist 1 5:8 15

or equivalently,

set geometry:actlist 1 5 6 7 8 15

If this option is not specified by entering a +SET+ directive, the default behavior in the code is to treat all atoms as active. To
revert to this default behavior after the option to define frozen atoms has been invoked, the +UNSET+ directive must be used (since
the database is persistent, see Section NWChem Architecture). The form of the +UNSET+ directive is as follows:

unset geometry:actlist

In addition, the Car-Parrinello module allows users to freeze bond lengths via a Shake algorithm. The following +SET+ directive shows how to do this.

set nwpw:shake_constraint "2 6 L 6.9334"

This input fixes the bond length between atoms 2 and 6 to be 6.9334 bohrs. Note that this input only recognizes bohrs.

When using constraints it is usually necessary to turn off center of mass shifting. This can be done by the following +SET+ directive.

set nwpw:com_shift .false.

Car-Parrinello Output Datafiles

XYZ motion file

Data file that stores ion positions and velocities as a function of time in XYZ format.

EIGMOTION motion file

Datafile that stores the eigenvalues for the one-electron orbitals as a function of time.

[line 1: ] time, (eig(i), i=1,number_orbitals)
[line 2: ] ...

OMOTION motion file

Datafile that stores a reduced representation of the one-electron orbitals. To be used with a molecular orbital viewer that will be ported to NWChem in the near future.

Born-Oppenheimer Molecular Dynamics

Metropolis Monte-Carlo

Free Energy Simulations

MetaDynamics

Metadynamics bias potential. Courtesy of Raymond Atta-Fynn

Metadynamics simulation of the first hydrolysis of U(IV) from [1]. Courtesy of Raymond Atta-Fynn

Metadynamics[2][3][4] is a powerful, non-equilibrium molecular dynamics method which accelerates the sampling of the multidimensional free energy surfaces of chemical reactions. This is achieved by adding an external time-dependent bias potential that is a function of user defined collective variables, . The bias potential discourages the system from sampling previously visited values of (i.e., encourages the system to explore new values of ). During the simulation the bias potential accumulates in low energy wells which then allows the system to cross energy barriers much more quickly than would occur in standard dynamics. The collective variable is a generic function of the system coordinates, (e.g. bond distance, bond angle, coordination numbers, etc.) that is capable of describing the chemical reaction of interest. can be regarded as a reaction coordinate if it can distinguish between the reactant, transition, and products states, and also capture the kinetics of the reaction.

The biasing is achieved by “flooding” the energy landscape with repulsive Gaussian “hills” centered on the current location of at a constant time interval Δt. If the height of the Gaussians is constant in time then we have standard metadynamics; if the heights vary (slowly decreased) over time then we have well-tempered metadynamics. In between the addition of Gaussians, the system is propagated by normal (but out of equilibrium) dynamics. Suppose that the dimension of the collective space is d, i.e. and that prior to any time t during the simulation, N + 1 Gaussians centered on are deposited along the trajectory of at times . Then, the value of the bias potential, V, at an arbitrary point, , along the trajectory of at time t is given by

where is the time-dependent Gaussian height. and W0 are width and initial height respectively of Gaussians, and Ttempered is the tempered metadynamics temperature. Ttempered = 0 corresponds to standard molecular dynamics because W(t) = 0 and therfore there is no bias. corresponds to standard metadynamics since in this case W(t) = W0=constant. A positive, finite value of Ttempered (eg. Ttempered=1500 K) corresponds to well-tempered metadynamics in which .

For sufficiently large t, the history potential will nearly flatten the free energy surface, , along and an unbiased estimator of F(s) is given by

Input

Input to a metadynamics simulation is contained within the METADYNAMICS sub-block. Listed below is the the format of a METADYNAMICS sub-block,

TAMD - Temperature Accelerated Molecular Dynamics

Input

Collective Variables

Bond Distance Collective Variable

Angle Collective Variable

This describes the bond angle formed at i by the triplet < jik > :

Coordination Collective Variable

The coordination number collective variable is defined as

where the summation over i and j runs over two types of atoms, ξij is the weighting function, and r0 is the cut-off distance. In the standard procedure for computing the coordination number, ξij=1 if rij < r0, otherwise ξij=0, implying that ξij is not continuous when rij = r0. To ensure a smooth and continuous definition of the coordination number, we adopt two variants of the weighting function. The first variant is

where n and m are integers (m > > n) chosen such that when rij < r0 and when rij is much larger than r0. For example, the parameters of the O-H coordination in water is well described by r0=1.6 Å, n = 6 and m = 18. In practice, n and m must tuned for a given r0 to ensure that ξij is smooth and satisfies the above mentioned properties, particularly the large rij behavior.

The second form of the weighting function, which is due to Sprik, is

In this definition ξij is analogous to the Fermi function and its width is controlled by the parameter . Large and small values of n respectively correspond to sharp and soft transitions at rij = r0. Furthermore ξij should approach 1 and 0 when rij < r0 and rij > > r0 respectively. In practice n=6-10 Å − 1. For example, a good set of parameters of the O-H coordination in water is r0=1.4 Å and n=10 Å − 1.

N-Plane Collective Variable

The N-Plane collective variable is useful for probing the adsorption of adatom/admolecules to a surface. It is defined as the average distance of the adatom/admolecule from a given layer in the slab along the surface normal:

where Zads denotes the position of the adatom/admolecule/impurity along the surface normal (here, we assume the surface normal to be the z-axis) and the summation over i runs over Nplane atoms at Zi which form the layer. The layer could be on the face or in the interior of the slab.

User defined Collective Variable

Frozen Phonon Calculations

Steepest Descent

The functionality of this task is now performed automatically by the PSPW and BAND. For backward compatibility, we provide a description of the input to this task.

The steepest_descent task is used to optimize the one-electron orbitals with respect to the total energy. In addition it can also be used to optimize geometries. This method is meant to be used for coarse optimization of the one-electron orbitals.

Input to the steepest_descent simulation is contained within the steepest_descent sub-block.

NWPW
...
STEEPEST_DESCENT
...
END
...
END

To run a steepest_descent calculation the following directive is used:

TASK PSPW steepest_descent
TASK BAND steepest_descent

The steepest_descent sub-block contains a great deal of input, including pointers to data, as well as parameter input. Listed below is the format of a STEEPEST_DESCENT sub-block.

Alternatively, instead of explicitly entering lattice vectors, users can enter the unit cell using the standard cell parameters, a, b, c, α, β, and γ, by using the LATTICE block. The format for input is as follows:

The user can also enter the lattice vectors of standard unit cells using the keywords SC, FCC, BCC, for simple cubic, face-centered cubic, and body-centered cubic respectively. Listed below is an example of the format of this type of input.

NWPW
...
SIMULATION_CELL SC 20.0
....
END
...
END

Finally, the lattice vectors from the unit cell can also be defined using the fractional coordinate input in the GEOMETRY input (see section Geometry Lattice Parameters). Listed below is an example of the format of this type of input for an 8 atom silicon carbide unit cell.

Warning - Currently only the "system crystal" option is recognized by NWPW. The "system slab" and "system polymer" options will be supported in the future.

Unit Cell Optimization

The PSPW module using the DRIVER geometry optimizer can optimize a crystal unit cell. Currently this type of optimization works only if the geometry is specified in fractional coordinates. The following SET directive is used to tell the DRIVER geometry optimizer to optimize the crystal unit cell in addition to the geometry.

set includestress .true.

SMEAR - Fractional Occupation of the Molecular Orbitals

The smear keyword to turn on fractional occupation of the molecular orbitals in PSPW and BAND calculations

Both Fermi-Dirac (FERMI) and Gaussian broadening functions are available. The ORBITALS keyword is used to change the number of virtual orbitals to be used in the calculation. Note to use this option the user must currently use the SCF minimizer. The following SCF options are recommended for running fractional occupation

SCF Anderson outer_iterations 0 Kerker 2.0

Spin Penalty Functions

Spin-penalty functions makes it easier to define antiferromagnetic structures. These functions are implemented by adding a scaling factor to the non-local psp for up/down spins on atoms and angular momentum that you specify.

AIMD/MM (QM/MM)

A QM/MM capability is available that is integrated with PSPW module and can be used with Car-Parrinello simulations. Currently, the input is not very robust but it is straightforward. The first step to run a QM/MM simulations is to define the MM atoms in the geometry block. The MM atoms must be at the end of the geometry and a carat, " ^ ", must be appended to the end of the atom name, e.g.

The option "mm_tags off" can be used to remove the " ^ " from the atoms, i.e.

NWPW
QMMM
mm_tags 6:11 off
END
END

Next the pseudopotentials have be defined for the every type of MM atom contained in the geometry blocks. The following local pseudopotential suggested by Laio, VandeVondele and Rothlisberger can be automatically generated.

The following input To define this pseudopo the O^ MM atom using the following input

NWPW
QMMM
mm_psp O^ -0.8476 4 0.70
END
END

defines the local pseudopotential for the O^ MM atom , where Z{ion} = − 0.8476, nσ = 4, and rc = 0.7. The following input can be used to define the local pseudopotentials for all the MM atoms in the geometry
block defined above

NWPW
QMMM
mm_psp O^ -0.8476 4 0.70
mm_psp H^ 0.4238 4 0.40
END
END

Next the Lenard-Jones potentials for the QM and MM atoms need to be defined. This is done as as follows

Note that the Lenard-Jones potential is not defined for the MM H atoms in this example. The final step is to define the MM fragments in the simulation. MM fragments are a set of atoms in which bonds and angle harmonic potentials are defined, or alternatively shake constraints are defined. The following input defines the fragments for the two water molecules in the above geometry,

PSP_GENERATOR

A one-dimensional pseudopotential code has been integrated into NWChem. This code allows the user to modify and develop pseudopotentials. Currently, only the Hamann and Troullier-Martins norm-conserving pseudopotentials can be generated. In future releases, the pseudopotential library (section Pseudopotential and PAW basis Libraries) will be more complete, so that the user will not have explicitly generate pseudopotentials using this module.

Input to the PSP_GENERATOR task is contained within the PSP_GENERATOR sub-block.

The following list describes the input for the PSP_GENERATOR sub-block.

<psp_name> - name that points to a.

<element> - Atomic symbol.

<charge> - charge of the atom

<mass> - mass number for the atom

<ncore> - number of core states

<nvalence> - number of valence states.

ATOMIC_FILLING:.....(see below)

<filling> - occupation of atomic state

CUTOFF:....(see below)

<rcore> - value for the semicore radius (see below)

ATOMIC_FILLING Block

This required block is used to define the reference atom which is used to define the pseudopotential. After the ATOMIC_FILLING: <ncore> <nvalence> line, the core states are listed (one per line), and then the valence states are listed (one per line). Each state contains two integer and a value. The first integer specifies the radial quantum number, n, the second integer specifies the angular momentum quantum number, l, and the third value specifies the occupation of the state.

For example to define a pseudopotential for the Neon atom in the 1s22s22p6 state could have the block

CUTOFF

This optional block specifies the cutoff distances used to match the all-electron atom to the pseudopotential atom. For
Hamann pseudopotentials rcut(l) defines the distance where the all-electron potential is matched to the pseudopotential, and for Troullier-Martins pseudopotentials rcut(l) defines the distance where the all-electron orbital is matched to the pseudowavefunctions. Thus the definition of the radii depends on the type of pseudopotential. The cutoff radii used in Hamann pseudopotentials will be smaller than the cutoff radii used in Troullier-Martins pseudopotentials.

For example to define a softened Hamann pseudopotential for Carbon would be

there are additional directives that are specific to the PSPW module, which are:

TASK PAW [Car-Parrinello || steepest_descent ]

Once a user has specified a geometry, the PAW module can be invoked with no input directives (defaults invoked throughout). There are sub-directives which allow for customized application; those currently provided as options for the PAW module are:

The pseudopotential libraries are continually being tested and added. Also, the PSPW program can read in pseudopotentials in CPI and TETER format generated with pseudopotential generation programs such as the OPIUM package of Rappe et al. The user can request additional pseudopotentials from Eric J. Bylaska at (Eric.Bylaska@pnl.gov).

Similarly, a library of PAW basis used by PAW is currently available in the directory $NWCHEM_TOP/src/nwpw/libraryp/paw_default

Currently there are not very many elements available for PAW. However, the user can request additional basis sets from Eric J. Bylaska at (Eric.Bylaska@pnl.gov).

A preliminary implementation of the HGH pseudopotentials (Hartwigsen, Goedecker, and Hutter) has been implemented into the PSPW module. To access the pseudopotentials the pseudopotentials input block is used. For example, to redirect the code to use HGH pseudopotentials for carbon and hydrogen, the following input would be used.

The implementation of HGH pseudopotentials is rather limited in this release. HGH pseudopotentials cannot be used to optimize unit cells, and they do not work with the MULLIKEN option. They also have not yet been implemented into the BAND structure code.

To read in pseudopotentials in CPI format the following input would be used.

nwpw
...
pseudopotentials
C CPI c.cpi
H CPI h.cpi
end
...
end

In order for the program to recognize the CPI format the CPI files, e.g. c.cpi have to be prepended with the "<CPI>" keyword.

To read in pseudopotentials in TETER format the following input would be used.

nwpw
...
pseudopotentials
C TETER c.teter
H TETER h.teter
end
...
end

In order for the program to recognize the TETER format the TETER files, e.g. c.teter have to be prepended with the "<TETER>" keyword.

If you wish to redirect the code to a different directory other than the default one, you need to set the environmental variable
NWCHEM_NWPW_LIBRARY to the new location of the libraryps directory.

NWPW RTDB Entries and Miscellaneous DataFiles

Input to the PSPW and Band modules are contained in both the RTDB and datafiles. The RTDB is used to store input that the user will need to directly specify. Input of this kind includes ion positions, ion velocities, and simulation cell parameters. The datafiles are used to store input, such the one-electron orbitals, one-electron orbital velocities, formatted pseudopotentials, and one-dimensional pseudopotentials, that the user will in most cases run a program to generate.

Ion Positions

The positions of the ions are stored in the default geometry structure in the RTDB and must be specified using the GEOMETRY directive.

Ion Velocities

The velocities of the ions are stored in the default geometry structure in the RTDB, and must be specified using the GEOMETRY directive.

Wavefunction Datafile

The one-electron orbitals are stored in a wavefunction datafile. This is a binary file and cannot be directly edited. This datafile is used by steepest_descent and Car-Parrinello tasks and can be generated using the wavefunction_initializer or wavefunction_expander tasks.

Velocity Wavefunction Datafile

The one-electron orbital velocities are stored in a velocity wavefunction datafile. This is a binary file and cannot be directly edited. This datafile is automatically generated the first time a Car-Parrinello task is run.

Formatted Pseudopotential Datafile

The pseudopotentials in Kleinman-Bylander form expanded on a simulation cell (3d grid) are stored in a formatted pseudopotential datafile (PSPW-"atomname.vpp", BAND-"atomname.cpp", PAW-"atomname.jpp"). These are binary files and cannot be directly edited. These datafiles are automatically generated.

One-Dimensional Pseudopotential Datafile

The one-dimensional pseudopotentials are stored in a one-dimensional pseudopotential file ("atomname.psp"). This is an ASCII file and can be directly edited with a text editor or can be generated using the pspw_generator task. However, these datafiles are usually atomatically generated.

Car-Parrinello Scheme for Ab Initio Molecular Dynamics

Car and Parrinello developed a unified scheme for doing ab initio molecular dynamics by combining the motion of the ion cores and a fictitious motion for the Kohn-Sham orbitals of density-functional theory (R. Car and M. Parrinello, Phys. Rev. Lett. 55, 2471, (1985) - simple introduction Media:Cpmd-lecture.pdf). At the heart of this method they introduced a fictitious kinetic energy functional for the Kohn-Sham orbitals.

Given this kinetic energy the constrained equations of motion are found by taking the first variation of the auxiliary Lagrangian.

Which generates a dynamics for the wavefunctions and atoms positions through the constrained equations of motion:

where μ is the fictitious mass for the electronic degrees of freedom and MI are the ionic masses. The adjustable parameter μ is used to describe the relative rate at which the wavefunctions change with time. Λij,σ are the Lagrangian multipliers for the orthonormalization of the single-particle orbitals . They are defined by the orthonormalization constraint conditions and can be rigorously found. However, the equations of motion for the Lagrange multipliers depend on the specific algorithm used to integrate
the Eqns. above.

For this method to give ionic motions that are physically meaningful the kinetic energy of the Kohn-Sham orbitals must be relatively
small when compared to the kinetic energy of the ions. There are two ways where this criterion can fail. First, the numerical integrations for the Car-Parrinello equations of motion can often lead to large relative values of the kinetic energy of the Kohn-Sham orbitals relative to the kinetic energy of the ions. This kind of failure is easily fixed by requiring a more accurate
numerical integration, i.e. use a smaller time step for the numerical integration. Second, during the motion of the system a the ions can be in locations where there is an Kohn-Sham orbital level crossing, i.e. the density-functional energy can have two states that are nearly degenerate. This kind of failure often occurs in the study of chemical reactions. This kind of failure is not easily fixed and requires the use of a more sophisticated density-functional energy that accounts for low-lying excited electronic states.

Verlet Algorithm for Integration

Integrating the Eqns. above using the Verlet algorithm results in

In this molecular dynamic procedure we have to know variational derivative and the matrix Λij,σ. The variational derivative can be analytically found and is

To find the matrix Λij,σ we impose the orthonormality constraint on to obtain a matrix Riccatti equation, and then Riccatti equation is solved by an iterative solution.

Constant Temperature Simulations: Nose-Hoover Thermostats

Nose-Hoover Thermostats for the electrons and ions can also be added to the Car-Parrinello simulation. In this type of simulation thermostats variables xe and xR are added to the simulation by adding the auxiliary energy functionals to the total energy.

In these equations, the average kinetic energy for the ions is

where f is the number of atomic degrees of freedom, kB is Boltzmann's constant, and T is the desired t
emperature. Defining the average fictitious kinetic energy of the electrons is not as straightforward.
Blöchl and Parrinello (P.E. Blöchl and M. Parrinello, Phys. Rev. B, 45, 9413, (1992)) have suggested the following formula for determining the average fictitious kinetic energy

where μ is the fictitious electronic mass, M is average mass of one atom, and is the kinetic energy of the electrons.

Blöchl and Parrinello suggested that the choice of mass parameters, Qe, and QR should be made such that the period of oscillating thermostats should be chosen larger than the typical time scale for the dynamical events of interest but shorter than the simulation time.

where P{ion} and P{electron} are the periods of oscillation for the ionic and fictitious electronic thermostats.

In simulated annealing simulations the electronic and ionic Temperatures are scaled according to an exponential cooling schedule,

where and are the initial temperatures, and τe and τionic are the cooling rates in atomic units.

Structural optimization of S2 dimer with LDA approximation

In this example, the structure of the S2 dimer using results generated from prior energy calculation is calculated. Since most of the parameters are already stored in the run-time database the input is very simple.

As the optimization process consists of series of total energy evaluations the contents of the output file are very much similar to that in Example I. At each step the total energy and force information will be outputed as follows

Frequency calculation of S2 dimer with LDA approximation

In this example, the vibrational frequency of the S2 dimer using results generated from prior geometry optimization is calculated. Since most of the parameters are already stored in the run-time database the input is very simple.

A plotting program (e.g. gnuplot, xmgrace) can be used to look at the total, potential, kinetic energies, contained in the s2-md.emotion file (see section EMOTION motion file for datafile format) i.e.,

seattle-1604% gnuplot
G N U P L O T
Version 4.0 patchlevel 0
last modified Thu Apr 15 14:44:22 CEST 2004
System: Linux 2.6.18-194.8.1.el5
Copyright (C) 1986 - 1993, 1998, 2004
Thomas Williams, Colin Kelley and many others
This is gnuplot version 4.0. Please refer to the documentation
for command syntax changes. The old syntax will be accepted
throughout the 4.0 series, but all save files use the new syntax.
Type `help` to access the on-line reference manual.
The gnuplot FAQ is available from
http://www.gnuplot.info/faq/
Send comments and requests for help to
<gnuplot-info@lists.sourceforge.net>
Send bugs, suggestions and mods to
<gnuplot-bugs@lists.sourceforge.net>
Terminal type set to 'x11'
gnuplot> plot "s2-md.emotion","s2-md.emotion" using 1:3
gnuplot>

The following plot shows the Car-Parrinello S2 energy surface generated from the simulation.

In principle quantum mechanical calculations can be used to determine the structure of any chemical system. One chooses a structure, calculates the total energy of the system, and repeats the calculation for all possible geometries. Of course the major limitation of this approach is that the number of local minima structures increases dramatically with system size and the cost of quantum mechanical calculations also increases dramatically with system size. Not surprisingly most quantum mechanical calculations limit the number of structures to be calculated by using experimental results or chemical intuition. One could speed up the calculations by using simplified inter-atomic force fields instead of quantum mechanical calculations. However, inter-atomic forces fields have many simplifying assumptions that can severely limit their predictability. Another approach is to use ab initio molecular dynamics methods combined with simulated annealing. These methods are quite robust and allow strongly interacting many body systems to be studied by direct dynamics simulation without the introduction of empirical interactions. In these methods, the atomic forces are calculated from ab initio calculations that are performed “on-the-fly” as the molecular dynamics trajectory is generated.

The following examples demonstrate how to use the ab initio molecular dynamics methods and simulated annealing strategies of NWChem to determine the lowest energy structures of the B12 cluster. This example is based on a study performed by Kiran Boggavarapu et al.. One might expect from chemical intuition that lowest energy structure of B12 will be an icosahedran, since B12 icosahedra are a common structural unit found in many boron rich materials. Despite this prevalence, ab initio calculations performed by several researchers have suggested that B12, as well as B and B, will have a more open geometry.

Simulated Annealing Using Constant Energy Simulation

This example uses a series of constant energy Car-Parrinello simulations with velocity scaling to do simulated annealing. The initial four Car-Parrinello simulations are used to heat up the system to several thousand Kelvin. Then the system is cooled down thru a series of constant energy simulations in which the electronic and ionic velocities are scaled by 0.99 at the start of each Car-Parrinello simulation. Energy minimization calculations are used periodically in this simulation to bring the system back down to Born-Oppenheimer surface. This is necessary because of electronic heating.

The Car-Parrinello keyword “scaling” scales the wavefunction and ionic velocities at the start of the simulation. The following input is used to increase the ionic velocities by a factor of two at the start of the Car-Parrinello simulation.

The program checks to see if the initial input ionic velocities have a non-zero center of mass velocity. If there is a non-zero center of mass velocity in the system then by default the program removes it. To turn off this feature set the following

Simulated Annealing Using Constant Temperature Simulation

The simulated annealing calculation in this example uses a constant temperature Car-Parrinello simulation with an exponential cooling schedule,

T(t) = T0e − t / τ

where T0 and τ are an initial temperature and a time scale of cooling, respectively. In the present calculations T0=3500K and τ=4.134e+4 au (1.0 ps) were used and the thermostat masses were kept fixed to the initial values determined by T=Te=3500K and (2π/ω)=250 a.u. (6 fs). Annealing proceeded for 50000 steps, until a temperature of 10K was reached. After which, the metastable structure is optimized using the driver optimizer.
The keyword SA_decay is used to enter the decay rates, τelectron and τion, used in the simulated annealing algorithm in the constant temperature car-parrinello simulation. The decay rates are in units of au (conversion 1 au = 2.41889e-17 seconds).

The development of a computational scheme that can accurately predict reaction energies requires some care. As shown in Table 1 energy errors associated with ab initio calculations can be quite high. Even though ab initio electronic structure methods are constantly being developed and improved upon, these methods are rarely able to give heat of formations of a broad class of molecules with error limits of less than a few kcal/mol. Only when very large basis sets such as the correlation-consistent basis sets, high level treatments of correlation energy such as coupled cluster methods (CCSD(T)), and small correction factors such as core-valence correlation energies and relativistic effects, are included will the heat of formation from ab initio electronic structure methods be accurate to within one kcal/mol. Although one can now accurately calculate the heats of formation of molecules with up to 6 first row atoms, such high-level calculations are extremely demanding and scale computationally as N7 for N basis functions.

Examples of these types of large errors are shown in the following Table, where the enthalpies of formation of CCl3SH are calculated by using atomization energies from different levels of ab initio theory.

Table 1: Standard enthalpy of formation (ΔH(298K) for CCl3SH in kcal/mol from atomization energies with various electronic structure methods. Results taken from reference [2].

MP2/cc-pVDZ

LDA/DZVP2

BP91/DZVP2

B3LYP/DZVP2

G2 Theory

ΔH

+4.9

-80.0

-2.6

+26.5

-13.0

Differences of up to 106.5 kcal/mol are found between different levels of theory. This example demonstrates that care must be taken in choosing the appropriate method for calculating the heats of formation from total atomization energies.

The difficulties associated with calculating absolute heats of formation from atomization energies can be avoided by using a set of isodesmic reactions[1]. The defining property of an isodesmic reaction - that there are an equal number of like bonds on the left-hand and right-hand sides of the reaction - helps to minimize the error in the reaction energy. These reactions are designed to separate out the interactions between molecular subsistents and non-bonding electrons from the direct bonding interactions by having the direct bonding interactions largely canceling one another. This separation is quite attractive. Most ab initio methods give substantial errors when estimating direct bonding interactions due to the computational difficulties associated with electron pair correlation, whereas ab initio methods are expected to be more accurate for estimating neighboring interactions and long-range through-bond effects.

The following isodesmic reaction can be used determine the enthalpy of formation for CCl3SH that is significantly more accurate than the estimates based on atomization energies.

CCl3SH + CH4 CH3SH + CCl3H, ΔHr(calc).

The first step is to calculate the reaction enthalpy of this reaction from electronic, thermal and vibrational energy differences at 298.15K at a consistent level of theory. The defining property of an isodesmic reaction that there are an equal number of like bonds on the left-hand and right-hand sides of the reaction helps to minimize the error in the calculation of the reaction energy. The enthalpy of formation of CCl3SH can then be calculated by using Hess’s law with the calculated enthalpy change and the experimentally known heats of formation of the other 3 species (see Table 3).

In this example, try to design and run NWPW simulations that can be used to estimate the enthalpy of formation for CCl3SH using its atomization energy and using the reaction enthalpy of the isodesmic reaction and compare your results to Table 2. Be careful to make sure that you use the same cutoff energy for all the simulations (.e.g. cutoff 35.0). You might also try to estimate enthalpies of formation for CHCl2SH and CH2ClSH. Also try designing simulations that use the SCF, DFT, MP2, and TCE modules.

CCl3SH + CH4 CH3SH + CCl3H

Un-optimized geometries for CCl3SH, CH3SH, CCl3H and CH4 which are needed to design your simulations are contained in the file Media:thermodynamics.xyz. You will also need to calculate the energies for the H, C, S, and Cl atoms to calculate the atomization energies. The multiplicities for these atoms are 2, 3, 3 and 2 respectively. You will also need to calculate the enthalpy of a molecule. The enthalpy of a molecule at 298.15K is sum of the total energy and a thermal correction to the enthalpy. A good estimate for the thermal correction to the enthalpy can be obtained from a frequency calculation, i.e.

NWPW Tutorial 4: AIMD/MM simulation of CCl4 + 64 H2O

In this section we show how use the PSPW module to perform a Car-Parrinello AIMD/MM simulation for a CCl4 molecule in a box of 64 H2O. Before running a PSPW Car-Parrinello simulation the system should be on the Born-Oppenheimer surface, i.e. the one-electron orbitals should be minimized with respect to the total energy (i.e. task pspw energy). In this example, default pseudopotentials from the pseudopotential library are used for C, Cl, O^ and H^, exchange correlation functional is PBE96, The boundary condition is periodic, and with a side length of 23.577 Bohrs and has a cutoff energy is 50 Ry). The time step and fake mass for the Car-Parrinello run are specified to be 5.0 au and 600.0 au, respectively.

NWPW Tutorial 5: Optimizing the Unit Cell and Geometry of Diamond

The PSPW and BAND codes can be used to determine structures and energies for a wide range of crystalline systems. It can also be used to generate band structure and density of state plots.

Optimizing the Unit Cell and Geometry for an 8 Atom Supercell of Diamond with PSPW

The following example uses the PSPW module to optimize the unit cell and geometry for a diamond crystal. The fractional coordinates and the unit cell are defined in the geometry block. The simulation_cell block is not needed since NWPW automatically uses the unit cell defined in the geometry block.

The C-C bond distance after the geometry optimization is 1.58 Angs. and agrees very well with the experimental value of 1.54 Angs.. Another quantity that can be calculated from this simulation is the cohesive energy.The cohesive energy of a crystal is the energy needed to separate the atoms of the solid into isolated atoms, i.e.

where Esolid is the energy of the solid and are the energies of the isolated atoms. In order to calculate the cohesive energy the energy of an isolated carbon atom at the same level of theory and cutoff energy will need to be calculated. The following input can be used to the energy of an isolated carbon atom.

Using this energy and energy of diamond the cohesive energy per atom is calculated to be

This value is substantially lower than the experimental value of 7.37eV! It turns out this error is a result of the unit cell being too small for the diamond calculation (or too small of a Brillioun zone sampling). In the next section, we show how increasing the Brillouin zone sampling reduces the error in the calculated cohesive energy.

The following figure shows a plot of the cohesive energy and C-C bond distance versus the Brillouin zone sampling. As can be seen in this figure the cohesive energy (w/o zero-point correction) and C-C bond distance agree very well with the experimental values of 7.37 eV (including zero-point correction) and 1.54 Angs.

Using BAND to Optimize the Unit Cell for a 2 Atom Primitive Cell of Diamond

In this example the BAND module is used to optimize a 2 atom unit cell for a diamond crystal at different Brillouin zone samplings.
The optimized energy and geometry will be (Monkhorst-Pack sampling of 11x11x11)

Using BAND to Calculate the Band Structures of Diamond

The following example uses the BAND module to calculate the band structure for the FCC cell of the a diamond crystal. The fractional coordinates and the unit cell are defined in the geometry block. The simulation_cell block is not needed since NWPW automatically uses the unit cell defined in the geometry block.

The following figure shows a plot of the cohesive energy and Ni-Ni bond distance versus the Brillouin zone sampling. As can be seen in this figure the cohesive energy (w/o zero-point correction) and Ni-Ni bond distance agree very well with the experimental values of 4.44 eV (including zero-point correction) and 2.49 Angs.

The following example uses the BAND module to optimize the unit cell and geometry for a Diamond crystal with Fd-3m symmetry. The fractional coordinates, unit cell, and symmetry are defined in the geometry block.

Optimizing Brucite, which is a soft layered material (2.5-3 Mohs scale), is more difficult to optimize than a hard material such as Diamond. For these types of materials using symmetry can often result in a faster optimization. For example, with symmetry the optimization converges within 20 to 30 geometry optimization steps,

NWPW Tutorial 9: Free Energy Simulations

A description of using the WHAM method for generating free energy of the gas-phase dissociation reaction CH3Cl CH3+Cl can be found in the attached pdf (Media:nwchem-new-pmf.pdf)

PAW Tutorial

Optimizing a water molecule

The following input deck performs for a water molecule a PSPW energy calculation followed by a PAW energy calculation and a PAW geometry optimization calculation. The default unit cell parameters are used (SC=20.0, ngrid 32 32 32). In this simulation, the
first PAW run optimizes the wavefunction and the second PAW run optimizes the wavefunction and geometry in tandem.

Running a Car-Parrinello Simulation

In this section we show how use the PAW module to perform a Car-Parrinello molecular dynamic simulation for a C2 molecule at the LDA level. Before running a PAW Car-Parrinello simulation the system should be on the Born-Oppenheimer surface, i.e. the one-electron orbitals should be minimized with respect to the total energy (i.e. task pspw energy). The input needed is basically the same as for optimizing the geometry of a C2 molecule at the LDA level,except that and additional Car-Parrinello sub-block is added.

In the following example we show the input needed to run a Car-Parrinello simulation for a C2 molecule at the LDA level. In this example, default pseudopotentials from the pseudopotential library are used for C, the boundary condition is free-space, the exchange correlation functional is LDA, The boundary condition is free-space, and the simulation cell cell is aperiodic and cubic with a side length of 10.0 Angstroms and has 40 grid points in each direction (cutoff energy is 44 Ry). The time step and fake mass for the Car-Parrinello run are specified to be 5.0 au and 600.0 au, respectively.